UGC NET Questions (Paper – 1)

Statements A and B correctly state the meanings of universal and existential quantifiers. Statement D gives the standard rule that the negation of a universal statement becomes an existential statement with negated predicate. Statement E is also true since many mathematical theorems and definitions are framed with such quantifiers. Statement C is false because ∀x P(x) and ∃x P(x) usually have very different truth conditions. Hence A, B, D and E only are correct.

Option A:
Option A is incomplete because it omits E and does not explicitly note the role of quantified statements in formulating general laws and existence results.

Option B:
Option B is wrong because it includes C, the incorrect claim that universal and existential forms are equivalent.

Option C:
Option C is incomplete because it omits A (meaning of ∀) and also does not collect the full correct set together.

Option D:
Option D is correct since it gathers all the true statements and rejects C, which conflates different quantifier types.

B, C, D and E are correct; A is false. The negation of “All S are P” is “Some S are not P”, not “No S are P”. B gives the correct negation of “Some S are P”. C and D are De Morgan’s laws. E is true about exam utility.

Option A:
Option A is incomplete because it omits E (which is true and relevant), so it does not include all correct statements.

Option B:
Option B is incorrect because it includes A, which gives the wrong negation of “All S are P”.

Option C:
Option C is correct because it includes all true statements (B, C, D, E) and excludes A (false).

Option D:
Option D is incorrect because it includes A, which is false, so it cannot be the correct set.